The concept of symmetric space is of central importance in many
branches of mathematics. Compactifications of these spaces have
been studied from the points of view of representation theory,
geometry, and random walks. This work is devoted to the study of
the interrelationships among these various compactifications and,
in particular, focuses on the martin compactifications. It is the
first exposition to treat compactifications of symmetric spaces
systematically and to uniformized the various points of view.
Key features:
* definition and detailed analysis of the Martin
compactifications
* new geometric Compactification, defined in terms of the Tits
building, that coincides with the Martin Compactification at the
bottom of the positive spectrum.
* geometric, non-inductive, description of the Karpelevic
Compactification
* study of the well-know isomorphism between the Satake
compactifications and the Furstenberg compactifications
* systematic and clear progression of topics from geometry to
analysis, and finally to random walks
The work is largely self-contained, with comprehensive
references to the literature. It is an excellent resource for both
researchers and graduate students.
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